Athenians used to stop off at Syntagma Square for the shopping, the shiny rows of upmarket boutiques. Now they arrive in their tens of thousands to protest. Swarming out of the metro station, they emerge into a village of tents, pamphleteers and a booming public address system.

Since 25 May, when demonstrators first converged here, this has become an open-air concert – only one where bands have been supplanted by speakers and music swapped for an angry politics. On this square just below the Greek parliament and ringed by flashy hotels, thousands sit through speech after speech. Old-time socialists, American economists just passing through, members of the crowd: they each get three minutes with the mic, and most of them use the time alternatively to slag off the politicians and to egg on their fellow protesters.

"Being here makes me feel 18 again," begins one man, his polo shirt stretched tight over his paunch, before talking about his worries about his pension.

The closer you get to the Vouli, the parliament, the more raucous it becomes. Jammed up against the railings, a crowd is clapping and chanting: "Thieves! Thieves!"

There is another mic here, and it's grabbed by a man wearing a mask of deputy prime minister Theodoros Pangalos: "My friends, we all ate together." He is quoting the socialist politician, who claimed on TV last year that everyone bore the responsibility for the squandering of public money. Pangalos may have intended his remark as the Greek equivalent of George Osborne's remark that "We're all in it together", but here they're not having it."You lying bastard!" They roar back. "You're so fat you ate the entire supermarket."

This is an odd alloy of earnestness and pantomime, to be sure, but it's something else too: Syntagma Square has become the new frontline of the battle against European austerity. And as prime minister George Papandreou battles first to keep his own job, and then to win MPs' support for the most extreme package of spending cuts, tax rises and privatisations ever faced by any developed country, what happens between this square and the parliament matters for the rest of the eurozone.

The banner wavers here know this. In the age of TV satellite vans and YouTube, they paint signs and coin slogans with half an eye on the export market. Papandreou's face is plastered over placards that congratulate him in English for being "Goldman Sachs' employee of the year". Flags jibe at the rive gauche: "The French are sleeping – they're dreaming of '68."

Most of the time, the anger is expressed sardonically. A friend shows me an app on her phone that gives updates on the latest political and industrial actions – its name translates as iStrike. But it's not hard to see how this situation might boil over.

"Are you an indignado?" I ask Nikkos Kokkalis, using the term coined by young Spanish protesters to express outrage at José Luis Rodríguez Zapatero's austerity plans, now swiped by the Greeks. "I'm a super-indignado," he almost shouts. A 29-year-old graduate who lives with his parents, Nikkos has never done a proper job – just menial tasks for a website and an internship for a TV station. "There are 300 people over there," he waves at the MPs' offices. "Most of them make decisions without asking the people."

For their part, protesters with salaries and wrinkles are fuming at the spending cuts already inflicted on them. Chryssa Michalopolou is a teacher who calculates that her annual pay has already gone down by the equivalent of one and a half months, while her living costs have shot up, thanks to rising taxes and inflation. Does she buy the government's line that it needs to trim the public sector? "After 15 years' service, I'm only on €1,200 (£1,056) a month," she says. "I didn't see any boom; I simply paid my taxes and now I am being punished."

On display here is more than a personal grievance; it also reveals a glaring truth that politicians across Europe have so far ignored. In their efforts to hammer out a second loan agreement for Greece, eurozone ministers are focusing on the differences between bond swaps and bond rollovers, the tensions between Berlin and the International Monetary Fund and the European Central Bank or how far continental banks can withstand another massive shock.

Taken for granted in these negotiations is that the Greeks (and by implication, the Irish and the Portuguese) must accept more austerity. Yet in Athens, whether on the streets or even at a policy-making level, these technical details barely figure on the agenda. It's not just that the terms are different, the entire debate is too. Here, the argument concerns how much more austerity the Greek economy, its people and even the government can take – because all three are already at breaking point.

When Greece was all but locked out of the financial markets last May, Papandreou accepted a €110bn loan from Europe and the IMF. The idea was that the money would tide the country over for a year, in which time his government would at least start sorting out its public finances. For Angela Merkel, Nicolas Sarkozy and the rest of Europe, the loan came with some pretty tight strings attached: they charged the Greeks interest well above the official eurozone rate, and set demanding budget targets for the Pasok socialist government.

Freefall

A year in, and the deal is not working. Greece has been in recession for two years and on official forecasts this will be its third. When I ask Athens University economist Yanis Varoufakis to describe the economy, he shoots back one sentence: "It's in freefall."

Sitting on the balcony of his flat behind the Acropolis, he throws out some statistics: 50,000 businesses went bankrupt last year, industrial production fell 20% and will drop another 12% this year. Unemployment has surged, so that one in six of the workforce doesn't have a job. These are the sort of figures associated with a depression, and the predictable result is that the public finances are getting worse. Greece's debt has ballooned to 153% of GDP; on Varoufakis's projections, even if ministers manage to make all their promised cuts, the government will owe three times the entire national income.

Behind these numbers lie the stories of a society in distress. One man talks about his daughter who works in the in-store restaurant of a large supermarket outside Athens; at closing time, she and her workmates have started giving out the unsold meals to the newly unemployed – the 21st-century equivalent of a soup kitchen. An employee of a local council notes that they pick up 17% less rubbish than a year ago, simply because people have cut back on food. The owner of an art gallery tells me her son has just started his first job; holding a master's in accountancy, he works six hours a day in a mobile-phone shop.

The lazy accusation to hurl at Greece is that it had a bloated public sector and so was bound to come a cropper. Not so, says Varoufakis: the country has a public sector in line with the rest of Europe (although, nearly everyone I speak to agrees, one that does not work as well), but takes in taxes some 35% below where they should be.

Wealthy Greeks have always treated the country's tax system like a church collection plate: what they give is strictly optional. This gap was covered up for as long as the Greek state could get cheap credit; then in 2008 it became glaringly obvious. The other problem covered up during the boom years was the rotting away of the industrial base. That too is now the subject of angry public discussion.

I take a tour of the shipbuilding yard in Perama, just outside Athens. Greece has the largest commercial fleet in the world, and yet Perama is utterly silent. There is a rusting hulk, abandoned a few years ago, when those who commissioned it could no longer afford to pay for it. A decade ago, this yard employed 7,000 workers – now it has around 500. There was a time when assembling small cargo vessels was seen as pedestrian work; last year, the yard was contracted to build two boats, and the jobs were fought over. A few minutes away lives Tassos Alexandris, who was laid off from Perama in 2008. The hall of his flat is decorated with needlepoint; inside are pictures of the Virgin Mary put up by his wife, Nikki. She is ill, and his 26-year-old daughter has worked for six months in her entire career. How do they make ends meet? Nikki snorts with laughter.

"The electricity connection is inside the flat; otherwise the board would have cut us off," begins Tassos. His mother-in-law lives upstairs and, while he is too ashamed to ask her for food, she allows him to raid her fridge at night. They had a small green Citroen, but couldn't afford to keep it. Now he runs a motorbike, although with no plates and no taxes. "I can't sleep at night for worry," he says. "It has affected every part of our lives: personal, sexual, the lot." How many families in this block do they think are in a similar situation? Nikki tots them up: "80%."

Tassos doesn't just support the protesters of Syntagma; he thinks they will go further. "Don't be surprised if Athens goes up in flames," the 50-year old says. "And don't be sad, either." His words initially sound melodramatic, but the anger keeps coming up. "Politicians now walk around with bodyguards," says Aris Chatzistefanou, the co-director of Debtocracy, a film about the Greek crisis that has become a sensation. He quotes a newspaper report of how restaurateurs are taking down those cheesy framed photos of dining politicians, of how one government spokesman went to dinner a few weeks ago only for the rest of the restaurant to start shouting "You are eating the blood of the people".

Political arithmetic

The anger against the austerity and the politicians imposing it is palpable; whether it will translate into political success is debatable. Papandreou may be one of the most hated men in Greece, but there is no mainstream politician who has an alternative to acting under creditor's orders. This isn't about an electorate taking on a government, either, but the impossible political arithmetic of disparate groups of Greeks on one side versus the IMF, the European Central Bank and 16 other eurozone members on the other.

Run that by the protesters of Athens, though, and even the older, more pragmatic ones have an answer. "We may lose," one grey-haired trade unionist said to me. "But what matters is how you lose."